( fi56 ) 



— {R -\- d) (l(p cos 

 and for A'B' totally 



- k, {R + d) (b, - 



^^■^(^^-(ïèr) 



C„ 



= -hb 



dt\ k,-{k~k,)d/E 



Of course as much heat is lost at the surface 5' C" as is conducted 

 towards A'B' ; and the melted and frozen quantities of ice and water 

 will therefore be equal. W being the quantity of heat that is required 

 for the melting of a gramme of ice, the melted quantity is 



■ K-''/r{K—K) 



_ KdpJo 



w. 



If 8^ is the specific gravity of ice, the volume of tliis quantity is : 





-^K 





On the other hand, if the cylinder moves with a uniform velocity 

 V a volume 



2Rv. 

 is melted. So we find for the value of v 



■^ k-d/j,(k,-k,) ^ 



_ 'k,+d/ji(k^-ky ' 



ydpJo 



RWSy 



To express b in the force P acting per unit of length of the 

 cylinder we have only to notice that an element EF ^ Rd<p is 

 acted on by a force per unit of surface^ co.'jy := (^;„ -|" ^ '^'^*" 9*) '^<'*' V- 

 Hence : 



P = 2 J (p„ cos <p -{- b cos'' if) Rd(p ^= TibR 







The velocity C in case P = 1 is found to be 



C = 



Ujo 





^K 



71 R' WS. 



(/)• 



We can find another expression for '^/n if we pay attention to the 

 motion of the water. If we concei\e the wire to be at rest but 

 the ice moving along it, we shall see at the limit A'B' water con- 

 tinually streaming into the channel ABA'B' while it streams out of 



